From U.S. Pat. No. 6,701,902 B2, a generic activated carbon filter is known which serves for binding the hydrocarbons diffusing out of a fuel tank and to subject them to a combustion process in a combustion engine. Since in case of activated carbon, the adsorption capacity for hydrocarbons is limited, such activated carbon filters have to be regularly purged after each loading with hydrocarbons. I contrast to the adsorption of hydrocarbons in the activated carbon of an activated carbon filter, a purging process in which the hydrocarbon portions are desorbed again by the activated carbon is supported by an increased temperature, for which reason the known activated carbon filter has a plate-shaped heating element which heats the activated carbon provided in the activated carbon filter in some areas to improve the desorption of the hydrocarbons.